scholarly journals Computation of Aerodynamic Damping for Flutter Analysis of a Transonic Fan

2011 ◽  
Author(s):  
Parthasarathy Vasanthakumar
Keyword(s):  
Phase Angle ◽  
Stokes Equations ◽  
Mode Shapes ◽  
Navier Stokes ◽  
Aerodynamic Load ◽  
Exchange Method ◽  
Flow Solver ◽  
Aerodynamic Damping ◽  
Transonic Fan ◽  
Operating Points

This paper describes the computational analysis of aerodynamic damping for prediction of flutter characteristics of a transonic fan stage that consists of a highly loaded rotor along with a tandem stator. Three dimensional, linearized Navier-Stokes flow solver TRACE is used to numerically analyse the flutter stability of the fan. The linear flow solver enables the modeling of a single blade passage to simulate the desired inter-blade phase angle. The unsteady aerodynamic load on a vibrating blade is obtained by solving the unsteady Navier-Stokes equations on a dynamically deforming grid and the energy exchange method is used to calculate the aerodynamic damping. The calculation of aerodynamic damping for the prediction of flutter characteristics of the fan rotor is carried out with and without considering the influence of the disk. The blade mode shapes from finite element modal analysis are obtained accordingly and the flutter calculations are carried out for three blade vibration modes at the design speed and at part speeds for all possible inter-blade phase angles. Two operating points, one on the working line and the other near stall are investigated at every rotational speed. Different aspects that affect the aerodynamic damping behaviour like part speed operation, variation in unsteady blade surface pressure fluctuation between operating points on the working line and at near stall and the corresponding variation in aerodynamic work, inter-blade phase angle etc., are described. This analysis primarily focuses on the variations in aerodynamic damping of the fan with and without the influence of the disk. In addition, influence and effect of shock wave on the aerodynamic damping is also discussed.

scholarly journals Flutter Analysis of a Transonic Fan

2002 ◽  
Author(s):  
R. Srivastava ◽  
M. A. Bakhle ◽  
T. G. Keith ◽  
G. L. Stefko
Keyword(s):  
Energy Exchange ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Exchange Method ◽  
Navier Stokes Equations ◽  
Aerodynamic Damping ◽  
Aeroelastic Analysis ◽  
Flutter Analysis ◽  
Blade Shape ◽  
Transonic Fan

This paper describes the calculation of flutter stability characteristics for a transonic forward swept fan configuration using a viscous aeroelastic analysis program. Unsteady Navier-Stokes equations are solved on a dynamically deforming, body fitted, grid to obtain the aeroelastic characteristics using the energy exchange method. The non-zero inter-blade phase angle is modeled using phase-lagged boundary conditions. Results obtained show good correlation with measurements. It is found that the location of shock and variation of shock strength strongly influenced stability. Also, outboard stations primarily contributed to stability characteristics. Results demonstrate that changes in blade shape impact the calculated aerodynamic damping, indicating importance of using accurate blade operating shape under centrifugal and steady aerodynamic loading for flutter prediction. It was found that the calculated aerodynamic damping was relatively insensitive to variation in natural frequency.

Applications of an Inviscid Q3D Linearized Flow Solver Towards the High Operating Line Flutter Region of a Transonic Fan

1998 ◽  
Author(s):  
Tomas J. Börjesson ◽  
Torsten H. Fransson
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Flow Solver ◽  
Operating Line ◽  
Flutter Boundary ◽  
Euler Model ◽  
Transonic Fan ◽  
Phase Angles ◽  
Operating Points

The capabilities of an inviscid quasi three-dimensional linearized unstructured flow solver to correctly predict the stall flutter limit, flutter modes and critical inter-blade phase angles on a transonic rotating shroudless fan model where experimental data exist have been investigated. Three operating points were chosen for investigation at 70% and 95% speed. At 70% speed two points were investigated: one close to the torsional flutter boundary (at the intermediate operating line) and one at the flutter boundary. The 95% speed point was at the flexural flutter boundary. Steady state and unsteady calculations were made at several stream sections per operating point. At each stream section unsteady calculations were performed over the entire range of inter-blade phase angles with different mode shapes (real mode, rigid torsion and rigid bending) at different frequencies. Thus the model was “provoked” with “unphysical” mode shapes and frequencies to be compared to the unsteady solution obtained with the mode shapes and frequencies observed from the experiments. Furthermore all unsteady calculations were made with different mesh densities and solutions from different “tuned” and “untuned” steady-state solutions. The main conclusion of the validation of the inviscid Q3D Euler model on the Fan C Model Rotating Rig is that the model generally predicts flutter, flutter modes and the critical inter-blade phase angles to be close to the experimentally determined ones.

Numerical Simulation of Transonic Fan Flutter With 3D N-S CFD Code

2008 ◽  
Author(s):  
Mizuho Aotsuka ◽  
Naoki Tsuchiya ◽  
Yasuo Horiguchi ◽  
Osamu Nozaki ◽  
Kazuomi Yamamoto
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Suction Surface ◽  
Navier Stokes Equations ◽  
Blade Loading ◽  
Flow Solver ◽  
Flutter Boundary ◽  
Transonic Fan ◽  
Volume Method

This paper describes the calculation of transonic stall flutter of a fan. A new CFD code has been developed and validated. The code is an unsteady 3D multi-block flow solver. The Reynolds-Averaged Navier-Stokes equations are solved using a finite volume method with Spallart-Allmaras 1 equation turbulence model. A grid deforming system is applied, so the new code is capable of simulating an oscillating blade row. This grid deforming system produces less grid distortion and the code has robustness for a blade oscillating calculation. The code has validated on an IHI’s research transonic fan rig test, and the result was in good agreement with the test data in the prediction of the flutter boundary. In the rig test at part-speed condition, stall-side flutter was experienced. In that condition, the inlet relative Mach number in the tip region is about unity. The aerodynamic work by the CFD at the near flutter condition is positive, which means that the flutter characteristic is unstable, while at other conditions the aerodynamic work is negative. The aerodynamic work increases rapidly just before the zero damping point with the increase of the blade loading. From the detailed CFD result, the shock wave on the suction surface contributes to the excitement of the blade oscillation, and the aerodynamic work of the shock wave has large value at the flutter condition.

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

scholarly journals Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

2004 ◽  
Vol 10 (5) ◽  
pp. 373-385
Author(s):  
Steffen Kämmerer ◽  
Jürgen F. Mayer ◽  
Heinz Stetter ◽  
Meinhard Paffrath ◽  
Utz Wever ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Flow Solver ◽  
Flow Simulations ◽  
Sensitivity Equations

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.

scholarly journals Determination of Aerodynamic Damping at High Reduced Frequencies

2018 ◽  
Author(s):  
Minghao Pan ◽  
Paul Petrie-Repar ◽  
Hans Mårtensson ◽  
Tianrui Sun ◽  
Tobias Gezork
Keyword(s):  
Acoustic Resonance ◽  
Forced Response ◽  
Economic Consequences ◽  
Navier Stokes ◽  
Flow Solver ◽  
Aerodynamic Damping ◽  
Acoustic Modes ◽  
Reduced Frequency ◽  
Standard Configuration

In turbomachines, forced response of blades is blade vibrations due to external aerodynamic excitations and it can lead to blade failures which can have fatal or severe economic consequences. The estimation of the level of vibration due to forced response is dependent on the determination of aerodynamic damping. The most critical cases for forced response occur at high reduced frequencies. This paper investigates the determination of aerodynamic damping at high reduced frequencies. The aerodynamic damping was calculated by a linearized Navier-Stokes flow solver with exact 3D non-reflecting boundary conditions. The method was validated using Standard Configuration 8, a two-dimensional flat plate. Good agreement with the reference data at reduced frequency 2.0 was achieved and grid converged solutions with reduced frequency up to 16.0 were obtained. It was concluded that at least 20 cells per wavelength is required. A 3D profile was also investigated: an aeroelastic turbine rig (AETR) which is a subsonic turbine case. In the AETR case, the first bending mode with reduced frequency 2.0 was studied. The 3D acoustic modes were calculated at the far-fields and the propagating amplitude was plotted as a function of circumferential mode index and radial order. This plot identified six acoustic resonance points which included two points corresponding to the first radial modes. The aerodynamic damping as a function of nodal diameter was also calculated and plotted. There were six distinct peaks which occurred in the damping curve and these peaks correspond to the six resonance points. This demonstrates for the first time that acoustic resonances due to higher order radial acoustic modes can affect the aerodynamic damping at high reduced frequencies.

Computational Hydrodynamics for an Autonomous Underwater Vehicle With Moving Control Surfaces

2002 ◽  
Author(s):  
Abdollah Arabshahi ◽  
Howard J. Gibeling
Keyword(s):  
Control System ◽  
Autonomous Underwater Vehicle ◽  
Stokes Equations ◽  
System Development ◽  
Underwater Vehicle ◽  
Time Dependent ◽  
Navier Stokes ◽  
Computational Hydrodynamics ◽  
Flow Solver ◽  
Control Surfaces

The present study was undertaken to provide information for both design improvement and control system development during various stages of an autonomous underwater vehicle (AUV) development project. The need to establish a predictive capability for the hydrodynamic (control) coefficients for an AUV presented an opportunity to apply a multiblock incompressible Navier-Stokes flow solver which has evolved over many years. The solver utilizes a state-of-the-art implicit, upwind numerical scheme to solve the time-dependent Navier-Stokes equations in a generalized time-dependent curvilinear coordinate system. Domain decomposition is accomplished via a general unstructured multiblock approach. In addition, an efficient grid movement capability is incorporated in the code that will handle the relative motion of a multi-component configuration (e.g. oscillating control surfaces). Numerous simulations were conducted during the course of this work. The computations for vehicle and propulsor design consisted mainly of steady state axisymmetric computations, while for control system development both steady and unsteady (prescribed motion) simulations were conducted. The latter cases focus on the forces and moments on the vehicle that are needed for extraction of control information. A brief overview will be presented on the flow solver. This will be followed by a presentation of the numerical results.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Forced Response Analysis of a Transonic Fan

2012 ◽  
Author(s):  
Parthasarathy Vasanthakumar ◽  
Paul-Benjamin Ebel
Keyword(s):  
Finite Element ◽  
Flow Field ◽  
Forced Response ◽  
Navier Stokes ◽  
Response Analysis ◽  
Aerodynamic Damping ◽  
Forcing Function ◽  
Transonic Fan ◽  
Work Done ◽  
Highly Loaded

The forced response of turbomachinery blades is a primary source of high cycle fatigue (HCF) failure. This paper deals with the computational prediction of blade forced response of a transonic fan stage that consists of a highly loaded rotor along with a tandem stator. In the case of a transonic fan, the forced response of the rotor due to the downstream stator assumes significance because of the transonic flow field. The objective of the present work is to determine the forced response of the rotor induced as a result of the unsteady flow field due to the downstream stator vanes. Three dimensional, Navier-Stokes flow solver TRACE is used to numerically analyse the forced response of the fan. A total of 11 resonant crossings as identified in the Campbell diagram are examined and the corresponding modeshapes are obtained from finite element modal analysis. The interaction between fluid and structure is dealt with in a loosely coupled manner based on the assumption of linear aerodynamic damping. The aerodynamic forcing is obtained by a nonlinear unsteady Navier-Stokes computation and the aerodynamic damping is obtained by a time-linearized Navier-Stokes computation. The forced response solution is obtained by the energy method allowing calculations to be performed directly in physical space. Using the modal forcing and damping, the forced response amplitude can be directly computed at the resonance crossings. For forced response solution, the equilibrium amplitude is reached when the work done on the blade by the external forcing function is equal to the work done by the system damping (aerodynamic and structural) force. A comprehensive analysis of unsteady aerodynamic forces on the rotor blade surface as a result of forced response of a highly loaded transonic fan is carried out. In addition, the correspondence between the location of high stress zones identified from the finite element analysis and the regions of high modal force identified from the CFD analysis is also discussed.

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